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Finite A5 height scaled

Proved
D1Bound5.finiteA5_height_scaled

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Actual integral A5 root-column height. No coefficient table or bound is an input hypothesis: all coefficients and the strict margin are proved.

Preamble
import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.Tactic
import Mathlib.Tactic.Convert
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteA5Matrix_Definitions

Formal statement
section
namespace D1Bound5










theorem _root_.D1Bound5.finiteA5_height_scaled (x y c : ℂ) (hy : y ≠ 0)
    (hxy : ‖x‖ ≤ ‖y‖) (hYC : 1000 ≤ ‖y‖*‖c‖) (i : Fin 3) :
    (101/100 : ℝ)*(‖finiteA5Left x y c i‖+‖finiteA5Right x y c i‖) <
      3113013*‖y‖^12*‖c‖^5 := by sorry

end D1Bound5
end
Source
D1Bound5/FiniteA5Height.lean, lines 65-87, SHA-256 66f6a82be0fc7c80701dbd448df9ae7c22b21b575492e209dfdf4672c73c0f48. Project: https://github.com/tomislav-math/d1-bound5-lean

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